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February 21st, 2017, 01:41 AM   #1
h80
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3D system to a 2D system coordinates conversion

Hi all,
I need help with a geometry problem for a computer program that I am developing:


  • I work in a 3D (x,y,z) Euclidian space - origin OO.
  • Within this space there is a 2D Euclidian plane with its own independent (x,y) coordinates system.
  • The 2D plane can be positioned anywhere within the 3D space.
  • Point A is defined by the intersection of a raycast form the 3D origin and the 2D plane.
  • I am able to get the 3D (x,y,z) coordinates of A and O, so I can compute the lengths [OO,A] and [OO,O].

I need to get the position of A within the 2D space (ie A(x,y)).

I might be able to get more data from my 3D engine, as I believe this is not quite enough? I'm losing my hair over this, I would really appreciate help working out how to go about this...
Does anyone know how I can work that out in a C# Unity script? (or other way?)

ps: I'm new here, let me know if I posted this in the wrong place?
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March 2nd, 2017, 08:59 AM   #2
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You say you are able to get length AO in the 2D plane but what is the orientation of the 2D coordinate system with respect to the 3D coordinate system? You need to specify that before you can get the 2D x and y coordinates of the point.
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